Paper Citation Record · LEDGER

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures

As of 16 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2501.02931.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.02931 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T22:06:47.178899Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

verified exact5
verified fuzzy14
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b334195d-25a3-434f-aff7-2947320ffddf · outbound

This paper cites TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:46.931077Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83079dde-981d-4ede-869c-3146aa7ba6c5 · outbound

This paper cites Metric Space Magnitude and Generalisation in Neural Networks.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Metric Space Magnitude and Generalisation in Neural Networks

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-10T22:06:47.625362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2c985d98-bc17-4288-8a2c-b4903a0865ee · outbound

This paper cites Convenient categories of smooth spaces.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Convenient categories of smooth spaces

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:48.101664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a98ea49b-aed0-4b10-bc1b-a7d8bd5d4f9a · outbound

This paper cites Automatic differentiation in machine learning: a survey.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Automatic differentiation in machine learning: a survey

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:46.962163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 58c735f0-13f8-413d-8660-4c30d6adc539 · outbound

This paper cites Cartesian differential categories.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Cartesian differential categories

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:48.058938Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 566d23d8-610b-439c-9531-e0ea4b0f52c6 · outbound

This paper cites Geometric Algebra Transformer.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Geometric Algebra Transformer

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:46.980508Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1a33bd8-4048-475e-beda-d58fc78f14b7 · outbound

This paper cites Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:46.988511Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87247190-a330-4a14-9b2d-c0c8ac224449 · outbound

This paper cites Towards Foundations of Categorical Cybernetics.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Towards Foundations of Categorical Cybernetics

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:46.996693Z

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Unavailable: canonical work link unavailable.

Observation be8bbb73-ef7c-4be4-a67b-fca624137c7e · outbound

This paper cites A Simple and Effective Positional Encoding for Transformers.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures A Simple and Effective Positional Encoding for Transformers

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.004124Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a30b74c-d36a-4123-9a6b-cbf185d40678 · outbound

This paper cites Differential structure, tangent structure, and sdg.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Differential structure, tangent structure, and sdg

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:48.040737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 589b5e61-1320-477b-aba6-8a7c265a152c · outbound

This paper cites Spherical CNNs.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Spherical CNNs

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.021667Z

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Observation 9dd41901-d867-4d6f-b017-a41e47b54e49 · outbound

This paper cites Categorical foundations of gradient-based learning.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Categorical foundations of gradient-based learning

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:48.018658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation f50501b7-a023-43f3-b9bd-cc6202b1ccb5 · outbound

This paper cites Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformers.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Euclidean, Projective, Conformal: Choosing a Geometric Algebra for Equivariant Transformers

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.036997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f4ecb1d-bde1-452f-a2d2-573311363ee2 · outbound

This paper cites Differentials and distances in probabilistic coherence spaces.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Differentials and distances in probabilistic coherence spaces

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.996196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 475e1cd5-8e84-4df5-abb7-6799de937c3b · outbound

This paper cites A mathematical framework for transformer circuits.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures A mathematical framework for transformer circuits

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.047919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4c1f73b-2c75-4e42-a251-4756075176aa · outbound

This paper cites Symmetry-driven graph neural networks.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Symmetry-driven graph neural networks

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-10T22:06:47.420941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9850aff9-cc26-4bdc-8e13-94b3b375c644 · outbound

This paper cites Backprop as functor: A compositional perspective on supervised learning.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Backprop as functor: A compositional perspective on supervised learning

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.965631Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 23831462-bb1f-41d5-820e-c50ff2f6ef37 · outbound

This paper cites Position: Categorical deep learning is an algebraic theory of all architectures.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Position: Categorical deep learning is an algebraic theory of all architectures

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.928982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d5acae68-4e54-432c-8ff0-430ece3b6b32 · outbound

This paper cites Marshall, Andrew S.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Marshall, Andrew S

Reference 19

Resolution: verified exact; raw_fallback, observed 2026-08-10T22:06:47.386267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 16abb223-3173-44b4-86a1-0e11f736eb2e · outbound

This paper cites 2-dimensional categories.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures 2-dimensional categories

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.895078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 6c9d1919-90f9-4ec8-aff3-da120e0f316b · outbound

This paper cites Categories enriched on two sides.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Categories enriched on two sides

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.868814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d73fa7ca-77b6-48a8-b39d-6c2d0224ba71 · outbound

This paper cites A 2-categories companion.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures A 2-categories companion

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.842397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation a61003cf-b0d0-4e9c-9494-0b1624c73882 · outbound

This paper cites Generalized Enrichment for Categories and Multicategories.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Generalized Enrichment for Categories and Multicategories

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-08-10T22:06:47.271926Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e8b5b000-e734-4223-9c0b-50715b3edd25 · outbound

This paper cites Categories for the working mathematician, volume 5.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Categories for the working mathematician, volume 5

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.816813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3408c9d8-af7c-4d10-8b89-8b656edc8a09 · outbound

This paper cites Pytorch: An imperative style, high-performance deep learning library.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Pytorch: An imperative style, high-performance deep learning library

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.128966Z

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Unavailable: canonical work link unavailable.

Observation abcdcfe0-30f8-4699-8ebd-295cfa1ad88e · outbound

This paper cites A survey of graphical languages for monoidal categories.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures A survey of graphical languages for monoidal categories

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.775459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 107ac9a9-1f71-4f65-8596-7f0cdc66f2b5 · outbound

This paper cites The formal theory of monads.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures The formal theory of monads

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.749353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation afa3c3cd-2020-4387-9f80-bae0b9a457ca · outbound

This paper cites Attention is all you need.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Attention is all you need

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.157892Z

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Unavailable: canonical work link unavailable.

Observation 2d05d79f-76ca-4496-b44b-e3086fe39a0a · outbound

This paper cites The Topos of Transformer Networks.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures The Topos of Transformer Networks

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-10T22:06:47.246186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation fda1632b-42b0-4cb0-8376-8e2795f5bcf9 · outbound

This paper cites Equivariant and coordinate independent convolutional networks.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Equivariant and coordinate independent convolutional networks

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T22:06:47.702874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 0fcf4043-5d93-4aec-8554-3256ceb848f4 · outbound

This paper cites Deep sets.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures Deep sets

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.173969Z

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Observation 2b33f5f7-7a21-4eb3-92d5-b384c8ca5aff · outbound

This paper cites write newline.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures write newline

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-10T22:06:47.178899Z

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Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.